We introduce two important concepts in the following. In many cases, the question of interest can be stated in terms of monotone comparative statics. Pdf priceinduced technical progress and comparative. Comparative statics analysis in economics world scientific. The study of the two equilibrium prices of onions is called comparative economic statics. The objective of this paper is to develop and apply some new results in the theory of monotone comparative statics. It does not study the motion towards equilibrium, nor the process of the change itself. From the demand function q nay bp, the inverse demand function price as a function of quantity sold is p aby qbn the profit function for the monopolist is then.
This paper presents some intuitive and directly usable results for such comparative statics. If we have enough information we can solve for the comparative static effects. Comparative statics,acornerstoneofeconomic analysis,enables prediction andunderstanding of economic effects by comparing equilibria before and after a change in a policy, exogenous carol horton tremblay is an associate professor at oregon state university email. Most of economic theory consists of comparative statics analysis. Impure public goods and the comparative statics of environmentally friendly consumption by matthew j. In such contexts, economists often have potential interest in the comparative statics of locally stable steadystates, with respect to the systems parameters. Distributional comparative statics martin kaae jensen july 16, 2015 abstract distributional comparative statics is the study of how individual decisions and equilibrium outcomes vary with changes in the distribution of economic parameters income, wealth, productivity, distortions, information, etc. Comparative statics in markets for indivisible goods. But it does not show how the new point of equilibrium i. Comparative statics analysis in economics san jose state university. Monotone comparative statics in situations like this where continuity and di erentiability assumptions of functions of parameters must be made to derive comparative statics, we can resort to the tool known as monotone comparative statics. Chris shannon gave a very interesting course on comparative statics in the fall 2002 that introduced me to the subject. Jan 17, 2017 3 comparative statics economics is all about comparative statics what happens to optimal economic choices if we change one parameter.
Supermodular comparative statics pawe l dziewulskiy l ukasz wo znyz march 2019. Lipsey, comparative statics involves a comparison of a. Comparative statics is a method used to analyse the result of changes in a models exogenous parameters by comparing the resulting equilibrium to the original one. Comparative statics in principalagent problems economics. Comparative statics and heterogeneity finn christensen towson university october 7, 2016 abstract this paper elucidates the role played by the heterogeneity of interactions between the endogenous variables of a model in determining the models behavior. Comparative statics in principalagent problems richard t.
It was, for example, the method used by hume 1752 in his analysis of an increase in the stock of gold on prices in an economy. Paczkowski rutgers university lecture 1 introduction to comparative economic systemsfall semester, 2008 1 59. Once the solutions are obtained, it is easy to find comparative statics. Albrecht, bertil holmlund and harald lang to be published in journal o f economic dynamie. Banana consumption and increase in price of banana. Comparative statics in managerial economics tutorial 30 march. Economic and comparative statics advance level economics. It is known that comparative statics are wellbehaved if these interactions.
Here the equilibrium price is determined at the level op 1 in comparative static economics the old and the new equilibrium positions are compared in the above figure, we can compare e and e 1 points of equilibrium. Department of economics, georgetown university bertil holmiund department of economics, uppsala university harald lang institute for international economic studies and department of economics, stockholm university abstract. However, this analysing method limits itself to comparing equilibriums, not analysing the reasons for the new equilibrium or the adjustment process. Mathematical economics is an approach to economic analysis, in which the economists make use of mathematical symbols in the statement of the problem and also draw upon known mathematical theorems to aid in reasoning. Generally, we distinguish between two types of comparative statics problems that.
Comparing economic outcomes both before and after a change in an underlying exogenous parameter. Generalized comparative statics for political economy models. Our comparative static analysis can be either quantitative or qualitative. Comparative statics in managerial economics tutorial 30. Abstract an important set of questions in economics concern how changes in the models exogenous parameters income, wealth, productivity, distortions, information, etc. Paczkowski lecture 1 introduction to comparative economic systems prof. Holden september 15, 2008 abstract principalagent problems are widespread in economics. Comparative statics analysis in economics most of economic theory consists of comparative statics analysis. Controlling invasive species population or spread to reduce the damage an invasive species causes after becoming established in a new habitat.
This article develops new tools to address such issues and illustrates their usefulness in applications. This result is obtained by simultaneously solving the equations for d6% and s8% to find the single price and quantity that satisfies both. Comparativestatics involves the determination of the e ect of changes in the value of an exogenous variableson thevalueof anendogenousvariable, e. Comparative statics in dynamic programming models with an application to job search by james w. The new demand curve d 1 d 1 intersects the supply curve ss on point e 1. Monotone comparative statics university of colorado boulder. Static analysis explains only the final state of equilibrium. The literature shows that many of the robust comparative statics results that arise in economic theory rely on three main properties.
By market outcomes, we mean the equilibrium price and the equilibrium. The first version of this paper was written at the singapore management university, which i visited in 2003. A comparative statics analysis tells how the monopoly price would be affected by changes in the exogenous variables n and y and in the parameters f and c. Comparative statics in dynamic programming models with an application to job search by james w albrecht. As a type of static analysis it compares two different equilibrium states, after the process of adjustment. Comparative statics eco4112f 2011 as weve said before, a key concept in economics is that of equilibrium. Pdf the comparative statics of equilibrium derivative prices. Explicit solution if we have enough information we can solve for the comparative static e ects explicitly. I am grateful to the economics department at uc berkeley, and in particular to robert anderson, for their hospitality. Kotchen department ofeconomics fernald house williams college williamstown, ma 01267 email. Comparative statics the study of how the solutions of an economic model change as the model parameters and specification are changed is important because 1 most of the testable predictions of economic theory are comparative statics predictions and 2 many economic equilibrium analyses are built from comparative statics.
A large part of the mathematical modelling we do in this regard is concerned with comparative statics, that is, the comparison of di erent equilibrium states that are associated with di erent sets. As an empirical science, economics employs theoretical models to describe economic phenomena and processes. Comparative statics is a tool used to predict the effects of exogenous variables on market outcomes. Economics is a social science that studies how to make decisions in face of scarce resources. Limitations of comparative statics economics assignment. Despite the prevalence of dynamic economic explanations, the formal analysis is static. The use of comparative statics, of comparing one equilibrium with another, is as old as economics itself. According to baumol, comparative static analysis can be used to show economic equilibrium before and after a change in one or more variables. Comparative statics is the determination of the changes in the endogenous variables of a. Dottia,1 adepartment of economics, university college london abstract the median voter theorem is an extremely popular result in political economy that holds only if the policy space is unidimensional.
It does not show how this new equilibrium has been reached. The ideal reader is approximately equally prepared in mathematics and economics. Comparative statics and heterogeneity towson university. Critical sufficient conditions are defined by splitting the economic model into a part that is isolated to be the focus of analysis and a second part about which we. Comparative statics with respect to changes in taste, cost and technology by anaba, sylvester anani page 2 comparative statics of change in taste, cost and technology abstract this paper contains an analytical but practical approach to the comparative statics. Extending the scope of monotone comparative statics results. Explicit solution if we have enough information we can solve for the comparative static e. Since it is usually believed little can be said in general settings mirrlees 1975, grossman and hart 1983 applied work typically uses the rstorder approach, justied by strong. Comparative static analysis in economics usually begins with still less explicit. Economic theory 16, 465469 2000 comparative statics of monopoly pricing tim baldenius1 and stefan reichelstein2 1 graduate school of business, columbia university, new york, ny 10027, usa email. Results for economic comparative statics of steady states of.
Exogenous variables shift either the market demand curve for example, news about the health effects of consuming a product or the market supply curve for example, weather effects on a crop. Comparative statics an overview sciencedirect topics. Then i present different tactics to do comparative statics, depending on how much algebraically complicated the model is. Comparative statics is the determination of the changes in the endogenous variables of a model that that will result from a change in the exogenous variables or parameters of that model. This paper presents a technique for qualitative comparative statics analysis in dynamic programming modeis. Comparative statics with respect to changes in taste, cost and technology by anaba, sylvester anani page 2 comparative statics of change in taste, cost and technology abstract this paper contains an analytical but practical approach to the comparative statics of changes in taste, cost and technology. Comparative statics eco4112f 2011 1 derivatives and rules of di erentiation for each of the functions below. Since mathematical economics is merely an approach to economic analysis, it should. Homogeneity of degree zero of marshallian demand 4. It was, for example, the method used by hume 1752 in. In economics, we are frequently interested in how solutions to a constrained optimization problem change when the economic environment changes.
Graduate school of economics, osaka university daiwa securities chair. Distributional comparative statics is the study of how individual decisions and equilibrium outcomes vary with changes in the distribution of economic parameters income, wealth, productivity, information, etc. The comparative statics of constrained optimization problems by john k. Comparative economic systems market systems libertarians monetarists keynesians industrial policy school advocates of income policy price and incomes control nonmarket systems indicative planning directive planning property, capitalism and socialism economic systems based on private property. Content articles in economics the neglect of monotone. The existing results on monotone comparative statics of equilibria can be summarized in the statementofmilgromand robertss1990,mrhereaftertheoremthatthe largestand smallest equilibria in a parameterized supermodular game are increasing in the parameter. The central topic is comparative statics for economics problems with many variables. Comparative statics of a changing demand or b changing supply. Lecture 1 introduction to comparative economic systems. Advance level economicsmeaning of economic staticmeaning of comparative staticseconomics on your tipsour books are now available on amazonspecial comboecon. We analyse the comparative statics of the equilibrium of economic models that weve. Impure public goods and the comparative statics of. The comparative statics of constrained optimization. Comparative statics of constrained optimization problems is a question at the heart of economic analysis.
Comparative statics analysis tells us how the equilibrium values of endogenous. In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous parameter. Comparative statics with multidimensional decision if the decision taken by the actor are multidimensional, new tools are needed to derive monotone comparative statics. This assumption restricts its use to a class of very simple problems.
Comparativestatic analysis in economics usually begins with still less explicit. Comparative statics for immigration johnson 1980 josh angrist mit 14. Notes on comparative statics, the oldfashioned way its. Monotone economic models tend to generate an interactions effect that has the same sign as the partial effect. Find the total derivative of each of the following with respect to t. He or she will have studied mathematics through vector calculus and linear algebra and have completed. Lipsey, comparative statics involves a comparison of a new equilibrium position with original equilibrium position due to change in some economic variable. Oftentimes we are not only interested in the optimizers themselves, but also how they will be a ected by changes in exogenous parameters. Though comparative static economic analysis has many drawbacks, yet it occupies an important role in economics. Feb 05, 2015 4 comparative statics introduction nicholson, ch. Paczkowski rutgers university fall semester, 2008 prof. Comparative statics is the determination of the changes in the endogenous variables of a model that that will reusult from a change in the exogenous variables or parameters of that model.
The analysis is illustrated with statistics and a survey of the evolution of capitalist economies since world war ii, along with critical observations on the neoclassical approach to economics. Comparative statics are statements about how solution to a problem changes with parameters. And comparative statics compares only the two final equilibrium states. A revision of comparative statics methodology in economics, or, how to do comparative statics on the back of an envelope. Only a few works have obtained comparative statics results in related dynamic economies. Section 5 identies the sense in which comparative static transitions are almost always. Marshallian demand and comparative statics ethan kaplan september 17, 2012. Monotone comparative statistics, with applications to. Results for economic comparative statics of steady states. A large part of the mathematical modelling we do in this regard is concerned with comparative statics, that is, the comparison of di erent equilibrium states that. This material is written for a halfsemester course in optimization methods in economics.
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